Handling Data 5

3 marks · Normal

Two fair coins are tossed. Explain, using probability, whether getting one head and one tail is more likely than getting two heads.

Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.

Show answer

Getting one head and one tail is more likely than getting two heads, as there are two outcomes (HT, TH) for one head and one tail but only one outcome (HH) for two heads.

Must show: List all possible outcomes OR a probability calculation

Also accept: States 'there are more ways to get one head and one tail than to get two heads' plus a correct calculation.

Common mistakes: Equating all outcomes with equal probabilities but not combining both HT and TH.

Show mark scheme and worked solution

Marking points

B1 · 1 mark · States all possible outcomes: HH, HT, TH, TT.

M1 · 1 mark · Identifies two outcomes for one head, one tail, and one for two heads.

A1 · 1 mark · Correctly concludes that one head and one tail is more likely, supporting with probability or count of outcomes.

Worked solution

Possible outcomes are:

HH, HT, TH, TT

Probability of two heads: 1/4

Probability of one head, one tail: HT or TH, each with 1/4, so total 1/4 + 1/4 = 1/2

1/2 > 1/4, so one head and one tail is more likely.